Yes, it is of course possible that you can acquire HSV 2 in both locations IF you gave oral sex to and had intercourse with the same person in the same encounter. But HSV 2 really doesn’t like the mouth very much and so it happens there less, recurs there less and shed far less than HSV 1 from the mouth. As you probably know, canker sores are not caused by herpes. And yes, you could try to recover virus from that mouth sore when you have it by PCR swabbing. But to me, it sounds like a classic canker sore.
I think for your presentation, HSV 2 is unlikely and I wouldn’t worry as much as you are about it because HSV 2 orally sheds and recurs so very infrequently. But if you want to try swabbing with an outbreak, you sure can.